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Tagged with prime-number-theorem fourier-analysis
2 questions
3
votes
0
answers
191
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What smoothing to use for PNT-like results?
Consider a Dirichlet series $\sum_n a_n n^{-s}$ with desirable analytic properties (e.g., analytic extension to $\Re s>0$); one example would be $a_n=\mu(n)$. Say we want to estimate $\sum_{n\leq x}...
10
votes
1
answer
808
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An extremal problem related either to an uncertainty principle on the circle, or else to the prime number theorem
Consider for $X = 1,2, \ldots$ the set $\mathcal{S}_X$ of trigonometric polynomials $f(t) := \sum_{|k| \leq X} c_k e^{2\pi i kt}$ on the circle $\mathbb{T} := \mathbb{R}/\mathbb{Z}$ of degree $\leq X$ ...